Algebra, Topology and Logic AdvanceS .
ATLAS is an informal research group, bringing together a number of research interests coalescing around the ILLC-UvA: algebraic logic, duality theory, modal logic, intuitionistic logic, point-free topology, logical model theory, and category theory. In my interpretation, it is brought together by two core principles:
Triangle: At the core of all of the work is a triangle between Logic, Algebra and Topology. Duality theory is the idea that algebra is better understood by letting it act on space, and that space is better understood by collecting pieces of it and forming algebraic operations on it. Algebraizability studies questions concerning how logical structures can be represented algebraically, and how one can “come back” from algebra to logic. Spatial semantics – broadly construed – have to do with how spaces and relational structures can be used as a semantics for logic.
The Structure of Logical Properties: Rather than study the model theory of logic, a lot of work in the vein of members of this group is concerned with studying classes of logic. This means that one is interested, beyond proving an interesting property of a logic (e.g., tabularity) in its distribution in whole lattices of logics (e.g., the existence of 5 pre-tabular intermediate logics.). This allows a rich understanding of the pecularity of such logical properties, which can be useful in applications of logical systems (e.g. interpolation in description logics).
Beyond that, the work is extremely diverse. Students (from the ILLC) interested in these areas are encouraged to take some specific courses in the subject (Intro to Modal Logic, Mathematical Structures in Logic) and courses which might benefit their broader understanding of the subject (Topics in Modal Logic, Dynamic Epistemic Logic, Category Theory, Model Theory). They are also encouraged to participate in the research projects which are occasionally offered at the ILLC.
The following is a list containing (some) of the frequent members of the ATLAS group at the ILLC-UvA, and associated institutions:
Senior Staff
PhD Students
Master Students
We meet bi-weekly. Meetings are in person in SP904. In the future we might set up hybrid participation
| Date | Speaker | Topic | Location | Time |
|---|---|---|---|---|
| 06/02/2023 | Rodrigo Almeida | Colimits of Heyting Algebras through Esakia Duality | F2.19 | 14h00-16h00 |
| 30/05/2023 | Qian Chen | Pretabular tense logics over S4t | F2.02 (ILLC) | 14h00-16h00 |
| 14/07/2023 | Brendan Dufty | Completeness for Conditional Intuitionistic Logic | F2.02 (ILLC) | 11h00-13h00 |